Decompositions of principal series representations of Iwahori–Hecke algebras for Kac–Moody groups over local fields

Auguste Hébert

Vol. 310 (2021), No. 2, 303–353

DOI: 10.2140/pjm.2021.310.303

Abstract

Recently, Iwahori–Hecke algebras were associated to Kac–Moody groups over non-Archimedean local fields. In a previous paper, we introduced principal series representations for these algebras and partially generalized Kato’s irreducibility criterion. Here, we study how some of these representations decompose when they are reducible and deduce information on the irreducible representations of these algebras.

Keywords

Kac–Moody groups, Iwahori–Hecke algebras, principal series representations, non-Archimedean local fields

Mathematical Subject Classification 2010

Primary: 20C08, 20G44

Secondary: 20E42, 22E50

Milestones

Received: 16 March 2020

Accepted: 15 December 2020

Published: 8 March 2021